CF2193D.Monster Game

You have been gifted a new game called "Elatyh". In the game, you are given $n$ swords, each with its own strength. In particular, the sword numbered $i$ has a strength of $a_i$. The game consists of $n$ levels, each of which features a monster.

You start at level $1$ and progress further. To pass level $i$ and move on to level $i + 1$, you need to defeat the monster at level $i$. To defeat the monster at level $i$, you need to deal it $b_i$ sword strikes. The swords in the game are very fragile, so they can only deal one strike before breaking. If you complete level $n$ or run out of swords, you can finish the game and proceed to score calculation.

Before the game, you are allowed to choose the difficulty level. If you choose difficulty $x$, swords with a strength less than $x$ will not affect the monsters. The game score in this case is equal to $x$ multiplied by the number of levels completed. Your task is to choose the game difficulty in such a way as to maximize the game score.

你获得了一款名为“Elatyh”的新游戏。在游戏中，你拥有 $n$ 把剑，每把剑都有其独特的强度。具体而言，编号为 $i$ 的剑的强度为 $a_i$。游戏共包含 $n$ 个关卡，每个关卡中都有一只怪物。

你从第 $1$ 关开始，逐关推进。要通过第 $i$ 关并进入第 $i+1$ 关，你需要击败第 $i$ 关的怪物。要击败第 $i$ 关的怪物，你需要对其施加 $b_i$ 次剑击。游戏中的剑非常脆弱，每次只能造成一次剑击便会损坏。若你成功通关第 $n$ 关，或耗尽所有剑，则游戏结束，进入计分阶段。

在游戏开始前，你可以选择游戏难度。若你选择难度 $x$，则所有强度小于 $x$ 的剑将无法对怪物造成任何影响。此时，你的游戏得分为：$x$ 乘以你所完成的关卡数。你的任务是选择一个合适的难度 $x$，使得游戏得分最大化。

Each test consists of several test cases. The first line contains a single integer $t$ ($1\le t\le 10^4$) — the number of test cases. The following describes the test cases.

The first line of each test case contains a single integer $n$ ($1\le n\le 2 \cdot 10^5$).

The second line of each test case contains $n$ integers $a_1, a_2, \dots, a_n$ $(1\le a_i\le 10^9)$.

The third line of each test case contains $n$ integers $b_1, b_2, \dots, b_n$ $(1\le b_i\le n)$.

It is guaranteed that the sum of the values of $n$ across all test cases does not exceed $2 \cdot 10^5$.

每个测试包含若干测试用例。第一行包含一个整数 $t$（$1\le t\le 10^4$），表示测试用例的数量。接下来描述各测试用例。

每个测试用例的第一行包含一个整数 $n$（$1\le n\le 2 \cdot 10^5$）。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$1\le a_i\le 10^9$）。

每个测试用例的第三行包含 $n$ 个整数 $b_1, b_2, \dots, b_n$（$1\le b_i\le n$）。

保证所有测试用例中 $n$ 的总和不超过 $2 \cdot 10^5$。

For each test case, output a single integer — the maximum game score.

对于每个测试用例，输出一个整数——游戏的最高得分。

Consider the first test case. Optimal difficulty to choose is $3$. If difficulty is $3$, you can deal strikes with swords number $2$ and $3$. With $2$ swords you can complete $1$ level, so the game score is $3\cdot 1 = 3$.

考虑第一个测试用例。最优选择的难度为 $3$。若难度为 $3$，则可使用编号为 $2$ 和 $3$ 的剑进行攻击。使用 $2$ 把剑可以完成 $1$ 个关卡，因此游戏得分为 $3\cdot 1 = 3$。